Unitary orbits of Hermitian operators with convex or concave functions

Bourin, Jean-Christophe; Lee, Eun-Young

doi:10.1112/blms/bds080

Cited by 65 publications

(30 citation statements)

References 23 publications

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“…The reconstruction of

boldG

from

boldK

is based on theoretical work in Refs. and . Of course, this approach is based on strong assumptions, namely that pleiotropy (and/or linkage) is widespread throughout the genome, allowing us to scavenge useful information on the structure of the

boldG

‐matrix by using smaller pieces of it.…”

Section: Cutting‐edge and Complex Models For Specific Phenotypic Traitsmentioning

confidence: 99%

Quantitative genetic methods depending on the nature of the phenotypic trait

Villemereuil

2018

Annals of the New York Academy of Sciences

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A consequence of the assumptions of the infinitesimal model, one of the most important theoretical foundations of quantitative genetics, is that phenotypic traits are predicted to be most often normally distributed (so-called Gaussian traits). But phenotypic traits, especially those interesting for evolutionary biology, might be shaped according to very diverse distributions. Here, I show how quantitative genetics tools have been extended to account for a wider diversity of phenotypic traits using first the threshold model and then more recently using generalized linear mixed models. I explore the assumptions behind these models and how they can be used to study the genetics of non-Gaussian complex traits. I also comment on three recent methodological advances in quantitative genetics that widen our ability to study new kinds of traits: the use of "modular" hierarchical modeling (e.g., to study survival in the context of capture-recapture approaches for wild populations); the use of aster models to study a set of traits with conditional relationships (e.g., life-history traits); and, finally, the study of high-dimensional traits, such as gene expression.

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“…The reconstruction of

boldG

from

boldK

boldG

‐matrix by using smaller pieces of it.…”

Section: Cutting‐edge and Complex Models For Specific Phenotypic Traitsmentioning

confidence: 99%

Quantitative genetic methods depending on the nature of the phenotypic trait

Villemereuil

2018

Annals of the New York Academy of Sciences

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“…where M.i/ D d iag.P i .z/P i .z/ı i;j /; 0 Ä j Ä n; and U i -unitary block matrices of order n C 1; 0 Ä i Ä n: For n D 1 the proof is contained in [8] (Lemma 3.4), for an arbitrary n the proof is similar. In view of the above, we obtain…”

Section: Criteria Of Complete Indeterminacymentioning

confidence: 63%

On the completely indeterminate case for block Jacobi matrices

Osipov

2017

Concrete Operators

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Abstract:We consider the infinite Jacobi block matrices in the completely indeterminate case, i. e. such that the deficiency indices of the corresponding Jacobi operators are maximal. For such matrices, some criteria of complete indeterminacy are established. These criteria are similar to several known criteria of indeterminacy of the Hamburger moment problem in terms of the corresponding scalar Jacobi matrices and the related systems of orthogonal polynomials.

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“…For partitions of positive matrices, the diagonal blocks play a special role. This is apparent in a rather striking decomposition due to the two first authors [2]:…”

Section: Two By Two Blocksmentioning

confidence: 97%

Positive matrices partitioned into a small number of Hermitian blocks

Bourin

Lee

Lin

2013

Linear Algebra and its Applications

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Positive semidefinite matrices partitioned into a small number of Hermitian blocks have a remarkable property. Such a matrix may be written in a simple way from the sum of its diagonal blocks: the full matrix is a kind of average of copies of the sum of the diagonal blocks. This entails several eigenvalue inequalities. The proofs use a decomposition lemma for positive matrices, isometries with complex entries, and the Pauli matrices.

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Unitary orbits of Hermitian operators with convex or concave functions

Cited by 65 publications

References 23 publications

Quantitative genetic methods depending on the nature of the phenotypic trait

Quantitative genetic methods depending on the nature of the phenotypic trait

On the completely indeterminate case for block Jacobi matrices

Positive matrices partitioned into a small number of Hermitian blocks

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